Equality (mathematics)

are not equal sets — the first consists of letters, while the second consists of numbers — but they are both sets of three elements and thus isomorphic, meaning that there is a bijection between them. For example

Equality of sets is axiomatized in set theory in two different ways, depending on whether the axioms are based on a first-order language with or without equality.

Incorporating half of the work into the first-order logic may be regarded as a mere matter of convenience, as noted by Lévy.